IJPAM: Volume 47, No. 2 (2008)

GENERALIZED ESSENTIALLY SLANT HANKEL OPERATORS

S.C. Arora$^1$, Jyoti Bhola$^2$
$^1$Department of Mathematics
University of Delhi
Delhi, 110 007, INDIA
e-mail: scarora@maths.du.ac.in
$^2$Department of Mathematics
Hansraj College
University of Delhi
Delhi 110 007, INDIA
e-mail: jbhola_24@rediffmail.com


Abstract.The notion of essentially slant Hankel operators is generalized to $k$-th order $(k\ge 2)$ essentially slant Hankel operators on the space $L^2(\TT)$, $\TT$ denoting the unit circle in the complex plane. The study is further carried to compressions of such operators. It is shown that for a fixed integer $k\ge 2$, a Rhaly operator is the compression of a $k$-th order essentially slant Hankel operator iff it is the compression of a $k$-th order essentially slant Toeplitz operator.

Received: May 16, 2008

AMS Subject Classification: 47B35

Key Words and Phrases: slant Hankel operator, essentially slant Hankel operator, Rhaly operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 2